Parameterized complexity in the polynomial hierarchy : extending parameterized complexity theory to higher levels of the hierarchy
著者
書誌事項
Parameterized complexity in the polynomial hierarchy : extending parameterized complexity theory to higher levels of the hierarchy
（Lecture notes in computer science, 11880 . Lecture notes in artificial intelligence . LNCS sublibrary ; SL1 . Theoretical computer science and general issues）（FoLLI publications on logic, language and information）
Springer, c2019
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注記
Bibliography: p. 387-396
Includes index
内容説明・目次
内容説明
Parameterized Complexity in the Polynomial Hierarchy was co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.
目次
Complexity Theory and Non-determinism.- Parameterized Complexity Theory.- Fpt-Reducibility to SAT.- The Need for a New Completeness Theory.- A New Completeness Theory.- Fpt-algorithms with Access to a SAT Oracle.- Problems in Knowledge Representation and Reasoning.- Model Checking for Temporal Logics.- Problems Related to Propositional Satisfiability.- Problems in Judgment Aggregation.- Planning Problems.- Graph Problems.- Relation to Other Topics in Complexity Theory.- Subexponential-Time Reductions.- Non-Uniform Parameterized Complexity.- Open Problems and Future Research Directions.- Conclusion.- Compendium of Parameterized Problems.- Generalization to Higher Levels of the Polynomial Hierarchy.
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